Transactions on Machine Intelligence

Transactions on Machine Intelligence

Design and Implementation of a Discrete-Time Unscented Kalman Filter (DTUKF) Based on Genetic Algorithm to Enhance the Performance of Nonlinear Navigation Systems

Document Type : Original Article

Authors
A. Talebi Sheikh Sarmast 1
N. Samadian 2
H. Zeinali 1
S. M. Mousavi Mirkalaei 3
1 Control Department, Faculty of Electrical Engineering, Shahid Beheshti University, Tehran, Iran
2 Electronics Department, Faculty of Electrical Engineering, Semnan University, Semnan, Iran
3 Professor, Electronics Department, Faculty of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran
10.47176/TMI.2020.64
Abstract
Nonlinear inertial navigation systems are considered among the most important navigation systems, featuring advantages such as independence from external communication, real-time speed and position calculation, and suitable bandwidth, making them very popular in vehicle navigation. These systems consist of an inertial measurement unit comprising three orthogonal accelerometers and three gyroscopes used to determine the position, speed, and direction of vehicle movement, calculating the vehicle''s position with minimal error over short distances. However, over time, due to errors in the gyroscopes and accelerometers and consecutive integrations of their outputs, the estimated position error increases. To achieve higher accuracy, especially in long-term navigation, a global positioning system (GPS) is used for its complementary properties with the inertial navigation system (INS). This paper discusses and analyzes the application of two Kalman filters linear Kalman filter and unscented Kalman filter on nonlinear navigation systems. A discrete-time unscented Kalman filter (DTUKF) is utilized to estimate the position, speed, and state of a nonlinear system, which in this case is an integrated navigation system. By accurately selecting a set of sigma points from a Gaussian distribution and propagating these points through the nonlinear function, estimation is performed with significantly higher accuracy. The unscented transformation allows for the selection of the distribution of these points and control of higher-order error using design parameters. Comparing this filter with the linear Kalman filter reveals the superior performance of the unscented Kalman filter due to not linearizing the nonlinear system, thereby reducing system error. Notably, this paper is the first to use a genetic algorithm to optimize the Q and R noise matrices to achieve minimal variance and optimal mean convergence to reference values.
Keywords
Genetic Algorithm
Nonlinear Inertial Navigation System
Extended Kalman Filter
Linear Kalman Filter
Unscented Kalman Filter
  • Pinti, P., Scholkmann, F., Hamilton, A., Burgess, P., & Tachtsidis, I. (2019). Current status and issues regarding pre-processing of fNIRS neuroimaging data: An investigation of diverse signal filtering methods within a general linear model framework. Frontiers in Human Neuroscience, 12. https://doi.org/10.3389/fnhum.2018.00505
  • Slussarenko, S., & Pryde, G. (2019). Photonic quantum information processing: A concise review. Applied Physics Reviews. https://doi.org/10.1063/1.5115814
  • Nunn, N. (2020). The historical roots of economic development. Science, 367. https://doi.org/10.1126/science.aaz9986
  • Telley, L., Agirman, G., Prados, J., Amberg, N., Fièvre, S., Oberst, P., Bartolini, G., Vitali, I., Cadilhac, C., Hippenmeyer, S., Nguyen, L., Dayer, A., & Jabaudon, D. (2019). Temporal patterning of apical progenitors and their daughter neurons in the developing neocortex. Science, 364. https://doi.org/10.1126/science.aav2522
  • Luengo, D., Martino, L., Bugallo, M., Elvira, V., & Särkkä, S. (2020). A survey of Monte Carlo methods for parameter estimation. EURASIP Journal on Advances in Signal Processing, 2020(1), 1-62. https://doi.org/10.1186/s13634-020-00675-6
  • Ade, P., Aghanim, N., Armitage-Caplan, C., Arnaud, M., Ashdown, M., Atrio-Barandela, F., Aumont, J., Baccigalupi, C., Banday, A. J., Barreiro, R. B., Bartlett, J. G., Battaner, E., Benabed, K., Benoit, A., Benoit-Lévy, A., Bernard, J.-P., Bersanelli, M., Bielewicz, P., Bobin, J., ... Zonca, A. (2020). Planck 2018 results. Astronomy & Astrophysics. https://doi.org/10.1051/0004-6361/201935891
  • Martin, D., Varsani, A., Roumagnac, P., Botha, G., Maslamoney, S., Schwab, T., Kelz, Z., Kumar, V., & Murrell, B. (2020). RDP5: A computer program for analyzing recombination in, and removing signals of recombination from, nucleotide sequence datasets. Virus Evolution, 7. https://doi.org/10.1093/ve/veaa087
  • Chen, Y., Chi, Y., Fan, J., & Ma, C. (2020). Spectral methods for data science: A statistical perspective. Foundations and Trends in Machine Learning, 14(4), 566-806. https://doi.org/10.1561/2200000079
  • Long, H., Zhang, L., Lv, M., Wen, Z., Zhang, W., Chen, X., Zhang, P., Li, T., Chang, L., Jin, C., Wu, G., Wang, X., Yang, F., Pei, J., Chen, P., Margueron, R., Deng, H., Zhu, M., & Li, G. (2019). H2A.Z facilitates licensing and activation of early replication origins. Nature, 577, 576-581. https://doi.org/10.1038/s41586-019-1877-9
  • Giannitrapani, A. (2011). Comparison of EKF and UKF for spacecraft localization via angle measurements. IEEE Transactions on Aerospace and Electronic Systems, 47(1), 75-84. https://doi.org/10.1109/TAES.2011.5705660
  • Zaho, D. (2006). Application of unscented Kalman filter in nonlinear geodetic problems. Global Information Application and Development Center of Beijing, China.
  • Faruqi, F. A., & Turner, K. J. (2000). Extended Kalman filter synthesis for integrated global positioning/inertial navigation systems. Journal of Applied Mathematics and Computation, 115(4), 213-227. https://doi.org/10.1016/S0096-3003(98)10068-1
  • Wang, W., Liu, Z.-Y., & Xie, R.-R. (2006). Quadratic extended Kalman filter approach for INS/GPS integration. Journal of Aerospace Science and Technology, 10(5), 709-713. https://doi.org/10.1016/j.ast.2006.03.003
  • Yu, M. J., Lee, J. G., & Park, C. G. (2004). Nonlinear robust observer design for strapdown INS in-flight alignment. IEEE Transactions on Aerospace and Electronic Systems, 40(1), 797-807. https://doi.org/10.1109/TAES.2004.1337455
  • Jamshaid, A., & Mirza, M. (2010). Performance comparison among some nonlinear filters for a low-cost INS/GPS integrated solution. Journal of Nonlinear Dynamics, 61(3), 491-502. https://doi.org/10.1007/s11071-010-9665-y
  • Grewal, M. S., & Andrews, A. P. (2001). Kalman filtering: Theory and practice using MATLAB (2nd ed.). Wiley. https://doi.org/10.1002/0471266388
  • Weiss, J. D., & Shields, F. (1998). GPS/INS integration in a severe urban environment. In IEEE Position, Location and Navigation Symposium, USA.
  • Yuan, G., & Zhang, T. (2009). Unscented Kalman filtering for ultra tightly coupled GPS/INS integration. In Proceedings of the IEEE International Conference on Mechatronics and Automation, Changchun, China.
  • Jwo, D. J., & Yang, C. (2013). Performance enhancement for ultra-tight for GPS/INS integration using a fuzzy adaptive strong tracking unscented Kalman filter. Journal of Nonlinear Dynamics, 73(1), 377-395. https://doi.org/10.1007/s11071-013-0793-z
  • Julier, S. J., Uhlmann, J. K., & Durrant-Whyte, H. F. (1995). A new approach for filtering nonlinear system. In Proceedings of the American Control Conference, Seattle, USA.
  • Julier, S. J., Uhlmann, J. K., & Durrant-Whyte, H. F. (2000). A new method for the nonlinear transformation of means and covariances in filters and estimators. IEEE Transactions on Automatic Control, 5(3), 477-482. https://doi.org/10.1109/9.847726
  • Julier, S. J., & Uhlmann, J. K. (2000). Reduced Sigma point filters for the propagation of means and covariances through nonlinear transformations. In Proceedings of the American Control Conference, Anchorage, USA.
  • Särkkä, S. (2007). On unscented Kalman filtering for state estimation of continuous-time nonlinear systems. IEEE Transactions on Automatic Control, 52(9), 1631-1641. https://doi.org/10.1109/TAC.2007.904453
  • Mariani, S., & Ghisi, A. (2007). Unscented Kalman filtering for nonlinear structural dynamics. Journal of Nonlinear Dynamics, 49(1), 131-150. https://doi.org/10.1007/s11071-006-9118-9
  • Masoumnezhad, M., Jamali, A., & Narimanzadeh, N. (2013). Optimal design of symmetrical/asymmetrical sigma-point Kalman filter using genetic algorithm. Transactions of the Institute of Measurement and Control, 37(3), 425-432. https://doi.org/10.1177/0142331214543092
  • Volpe, J. (2001). Vulnerability assessment of the transportation infrastructure relying on the Global Positioning System. National Transportation Systems Center, USA.
  • Wang, G., Han, Y., Chen, J., Wang, S., Zhang, Z., Du, N., & Zheng, Y. (2018). A GNSS/INS integrated navigation algorithm based on Kalman filter. IFAC-Papers-Online, 52(17), 232-237. https://doi.org/10.1016/j.ifacol.2018.08.151
  • Forssell, B. (1991). Radio navigation systems. Prentice-Hall.
  • Lawrence, A. (1993). Modern inertial technology: Navigation, guidance, and control. Springer-Verlag.
  • Jwo, D. J., & Chung, F. (2010). Fuzzy adaptive unscented Kalman filter for ultra-tight GPS/INS integration. In International Symposium on Computational Intelligence and Design, Hangzhou, China. https://doi.org/10.1109/ISCID.2010.148
  • Zhai, X., Qi, F., Zhang, H., & Xu, H. (2012). Application of unscented Kalman filter in GPS/INS. In International Symposium on Photonics and Optoelectronics, Shanghai, China. https://doi.org/10.1109/SOPO.2012.6270470
  • Hu, Y., Liu, K., Zhang, X., Su, L., Ngai, E. W. T., & Liu, M. (2015). Application of evolutionary computation for rule discovery in stock algorithmic trading: A literature review. Applied Soft Computing, 36, 534-551. https://doi.org/10.1016/j.asoc.2015.07.008
  • Aleti, A., & Grunske, L. (2015). Test data generation with a Kalman filter-based adaptive genetic algorithm. Journal of Systems and Software, 103(1), 343-352. https://doi.org/10.1016/j.jss.2014.11.035
Transactions on Machine Intelligence
Volume 3, Issue 2
Spring 2020
Pages 64-80

  • Receive Date 10 February 2020
  • Revise Date 14 April 2020
  • Accept Date 05 June 2020